Yes, you not only have a case for personal injury for your daughter's injuries, but you likely have a claim under the Uniform Commercial Code (UCC) for damages.
The UCC is a part of the law that few attorneys are familiar with. It's something they study for the bar and never deal with again. I haven't personally looked at it in years, but years and years ago I had a case involving a cat breeder, and that was covered.
Since this matter involves two states, I wouldn't suggest Small Claims Court - plus, you wouldn't get very much that way.
I suggest that you find a personal injury attorney in a large office (more resources), and an office that can handle UCC (or at least look into that for you).
In Virginia, you can find such attorneys through here: http://www.vtla.com/VA/
Or, in NC, you can find attorneys here: http://www.ncaj.com/
There is an additional option, but it would probably just cover the cost of the horse, nothing more. That's to file a consumer protection complaint in Virginia. http://www.oag.state.va.us/CONSUMER/index.html And/or file with the federal agency, which is fcc.org, if memory serves.
If it were me, I'd first looking into hiring an attorney in this particular instance. I just wanted to let you know all your options.
I wish your daughter a speedy recovery.
I'm going to take a break for about an hour, and will check back then for further questions, if any.